Investigations Ineffective At Teaching Math

At least according to the independent research conducted by the Institute of Education Sciences.

The survey looked at four elementary mathematics curricula – Saxon, Math Expressions, Investigations, and SFAW. Among the conclusions noted are:

• Student math achievement was significantly higher in schools assigned to Math Expressions and Saxon, than in schools assigned to Investigations and SFAW.
• Math achievement in the two more effective curricula was not significantly different, nor was math achievement in schools assigned to the less effective curricula.

The researchers sought to determine whether the different curricula perfromed better under different circumstances – for instance was one more effective in districts with large portions of students on free and reduced lunches, or did large amounts of teacher professional development play a role in student performance.  The researchers found that there were no instances where Investigations or SFAW demonstrated a statistical advantage over Saxon or Math Expressions.

Perhaps that explains why TERC needed an NSF grant to develop their curricula, an NSF grant to develop programs to market and sell their curricula to school districts, an NSF grant to develop program to convince parents of how wonderful the curricula is, an NSF grant to develop a program whereby teachers become TERC Math Specialists, and multiple NSF grants to help school districts pay for the curricula.  See, if the program was effective at all schools would be clamoring to buy it.  Since it isn’t effective and no independent, verifiable studies have ever been conducted to demonstrate it’s effectiveness, TERC had to find a different way to sell their curricula.  They found it when the NSF ponied up taxpayer money to develop the program, market it to school districts, pay for teacher professional development, and purchase the instructional materials.  Why else would any school distrcit choose to a substandard program like Investigations – unless it was free?

You can find the entire study here.

TERC’s Bogus Studies

For parents who believe Investigations isn’t right for their children, this report will come as no surprise. For others, however, discovering that the “research” that underlies Investigations isn’t based on scientific protocols and that no independent studies have ever verified the publisher’s claims of success, might be a bit shocking.

From the “What Works ClearningHouse”, a Division of the US Department of Education Institute of Education Sciences…

“No studies of Investigations in Number, Data, and Space® that fall within the scope of the Elementary School Math review protocol meet What Works Clearinghouse (WWC) evidence standards. The lack of studies meeting WWC evidence standards means that, at this time, the WWC is unable to draw any conclusions based on research about the effectiveness or ineffectiveness of Investigations in Number, Data, and Space®. “

You can find the full report here.

The Opt in Proposal

Mr Trenum has proposed an Opt In for Traditional Math to the school board.

The Proposal

That the Prince William County School Board approve:

That, every parent, upon enrollment of their children in elementary school, will be notified of and given an opportunity to select the mathematics instructional model that they prefer for their children: a classical model based on a traditional math curriculum, a reform-based model based on the Math Investigations curriculum or No Preference. Any children whose parents do not select an option will be considered to be No Preference.

Students whose parents respond that they prefer a particular program will be enrolled in that program. Students whose parents select No Preference will be assigned to an instructional program by the principal as necessary to balance out class sizes.

Students whose parents choose either the classical instructional model or the reform-based instructional model are expected to remain in that program until they complete elementary school or transfer out of the PWCS system. Once a choice is made, re-enrollment each subsequent year will not be required.

Transferring from one program to another will be approved by the principal and will only be permitted if good cause is demonstrated. No Preference students will be given one opportunity to transfer from their assigned program without demonstrating cause. Parents who wish to transfer from one program to the other must notify their school in writing before the end of the current school year. Transfers will normally be effective at the start of the following school year, and will only be permitted in the middle of the school year if adequate space exists in the desired program to accommodate the additional students.

Students who enroll in the classical mathematics course of instruction will be provided with traditional textbooks, either from existing inventories or newly purchased if necessary. Schools will be permitted to select instructional materials for the classical program that they believe best meet their students needs from the list of VA DOE approved textbooks.

Commentary
The only possible negative with this proposal is that it creates two instructional programs in PWC schools. Unfortunately, given central office staff’s complete commitment to and belief in the Investigations approach, I tend to think that any approach which leaves central office staff in control of instructional content will further the mandate to adhere to Investigations. This approach allows central office to mandate content in the Investigations program, grants teachers the flexibility to develop programs they believe will meet their students needs, and allows parents to choose which approach they believe will best meet their children’s needs.

The Blended Proposal

NOTE:  We have heard reports that the proposal has been revised and the language requiring that two textbooks be provided to every student has been removed.  The revised proposal has not been posted to the PWCS web site, however, we will post it the moment it is.

At the February 18th board meeting Dr Otaigbe, the school board representative from Coles District, presented a motion regarding mathematics in PWC.

The Proposal

Under the supervision of the Superintendent, Prince William County
Public Schools will implement a consistent blended approach to
mathematics education with the following elements:

1. The goal at each grade level is to achieve the mathematics
objectives of the Virginia Standards of Learning and the PWCS
curriculum.

2. All students are expected to achieve computational fluency
and understanding of mathematics concepts appropriate for that grade
level.

3. Math Investigations textbooks and traditional math workbooks
will be provided for all students to support a blended approach to
the teaching of mathematics.

4. Classroom teachers will have the flexibility to use
instructional materials as appropriate to achieve learning outcomes.

5. The mathematics program will be implemented in the spirit of
site-based management.

6. Success of the program will be evaluated by scores on SOL and
other achievement tests, by student readiness for advanced math
courses, and by survey responses from parents and staff members.

7. Advanced students will be further challenged with additional
or more complex problems and activities offered in each classroom.

The Pros and Cons

I think there’s a huge disconnect between the intent of the proposal and the actual wording of it.  And, as we’ve seen may many times before, unless the board is absolutely specific with what it expects, the school system will do whatever it wants.

The intent of the proposal is to return control over content to the teachers – it allow them to select whatever materials they believe are best for their students and teach from those materials. I agree with this idea, in theory, however, I have several very large concerns with it.

The first is how the proposal is written.  If the intent I described above is accurate, then the wording of the proposal needs to say so explicitly.  The impression of the proposal, based on feedback from teachers, is that this proposal is nothing more than the status quo.  That we’ll continue with the empty claims of a blended program with central office dictating what lessons are taught, when they’re taught, and with what material and that is all Investigations all the time.

Teachers will be even further intimidated to keep their mouths shut and support the school system and parents who dare to present evidence that the program has not changed will be further castigated as the liars and manipulators we’re repeatedly called by school staff and board members now.

My second concern is cost.  Providing every child with both Investigations and traditional materials will increase our materials costs roughly $1.7 million more then we’re currently budgeted to spend over the next 4 years for math materials – an increase of $850,000 just this year.  Cost is definitely a concern in these budgetary times.

My third concern is consistency of delivery.  The two approaches are markedly different with vast chasms in the expectations for what a student will have learned at the end of each grade level.  A3rd grade traditional teacher will expect her students to know and be familiar with the standard algorithms and to have mastered their addition and subtraction math facts.  But Investigations doesn’t even expose students to the standard algorithms for addition and subtraction until Grades 4 and 5. The net effect is that teachers will have spend considerable time in the beginning of each year providing remedial lessons to those students who have never been taught under the approach she prefers.

My fourth concern is class assignments.  We all know how it works at schools.  Parents find out which teachers do X or Y  and parents who want their children taught X or Y try to get their children in those classes.  If this program is implemented, parents who prefer a traditional math education for their children will do everything they can to get their children assigned to a traditional teacher and will scream and yell when that doesn’t happen.    The net effect, at some schools, will be two instructional tracks with parents fighting to get their children in with the teachers who teach in the approach they prefer, while other schools will have parents, teachers, and Principal’s fighting tooth and nail over classroom assignments.

The fifth concern is that program is almost identical to the program we had before Investigations was mandated county wide.  I find it interesting that the board member who so often rants about how horrible our program was before, actually  supports this option because it is virtually identical to the program he routinely lambastes as terrible.

Traditional Math Proposals – Speak Up!

Things are moving pretty fast on the front to restore traditional math to PWC schools.

There are two proposals regarding traditional math in front of the school board. The first if by Mr Trenum and grants parents a choice in how their children are taught mathematics. You can find that proposal here. The second is by Dr Otaigbe and it will compel the school system to purchase two sets of instructional materials for all students while allowing the Superintendent and central office staff to maintain control over curriculum. You can find that proposal here.

The Opt in, in my opinion, is the only approach which will give our children a chance to learn real math. Dr Otaigbe’s proposal has not changed significantly from it’s original state and, in my opinion, will change nothing.

If you want a say in how your children are taught math you need to speak up now and send your comments to the school board.

Discussion of each of these proposals can be found at the following articles on our blog:

Why we oppose the Blended Approach

Comments on The Opt In (previously know as the choice option)

Comments on The Blended Approach (Dr Otaigbe’s proposal)

Cost Estimates for each

Click here to send an email to the entire school board.

URGENT – Action Needed !!!!!

If you thought the fight to restore traditional math to PWC elementary schools was about to end, you’d be wrong – and we need your help.

Dr Otaigbe has proposed a motion to provide a Blended Approach to mathematics in PWC schools, which he sincerely and honestly believes will fix the problem. In my opinion, the proposal, as currently written, solves nothing and reinforces the hollow promises of a blended program we’ve been hearing for over a year. Unfortunately a large number of board members seem to have been swayed by illusions of a Blended Approach and appear to be more than willing to support this empty promise.

Mr Trenun has proposed the Opt In for Traditional math which would provide each of us with a choice in how our children are taught math. Unfortunately, Dr Otaigbe’s blended proposal appears to have more support from board members. We need your help if we’re to defeat the blended proposal and provide choice for our children.

For more information about the proposals, please read them and our assessment of each here.

The Blended Approach, which appears to have the most support on the board and is likely to be approved unless a huge number of us inform the board of our concerns with it, puts the Superintendent and central office staff in charge of defining and ensuring that all schools provide a blended approach to math which will be accomplished by requiring that every student be given both a traditional textbook / workbook and an Investigations workbook.

The approach ignores the fact that for the past year and half the Superintendent and central office staff have been in charge of the math program and have been telling us that the program was blended. If they weren’t telling the truth then, and haven’t been delivering the blended program they claim they were, why should we believe they’ll change it now?

The proposal also calls for every student to be given both a traditional textbook / workbook and an Investigations workbook. Just giving each child a textbook doesn’t mean they child will actually be taught lessons from the textbook. The pacing of the lessons and what material is used to teach it comes from the math department. Just who will be tasked with developing the new “blended” pacing guides?  The math department.  The same department which comprised of Investigations true believers, has stated repeatedly that a blended approach is dangerous, and has been falsely claiming that they teach a blended approach for over a year now.

Does anyone honestly believe they’ll adapt the lesson pacing so that they reflect a true blend of material from both instructional approaches?

The school system is $57 million in the hole now. Purchasing two sets of materials will double our materials costs by more than $1.7 million over current spending over a 4 year period. Where is the school system supposed to find the money to buy those materials?

I can’t help but wonder why we haven’t heard a single statement defining what a blended approach or blended curriculum is. After all, the Superintendent and central office staff have repeatedly told the school board and parents that a blended approach is IMPOSSIBLE and possibly HARMFUL. I think hearing from them just what constitutes a blended approach, and why they believe it could be effective when they’ve so forcefully stated that it’s dangerous,  is imperative.

The school board needs to hear from you.  Today.  They need to know what you think.  They will approve this motion, which solves nothing, unless you let them know what you think.  So tell them.  Here’s a link to send a message to the entire board.

Evidence of Success – Then vs. Now

UPDATED

The PWCS web site includes a link to “Success in Other School Districts”, a report prepared by Investigations publisher which claims success in approximately 70 school districts across the country with Math Investigations.

One parent set out to independently verify those success stories and see how Investigations was doing in those districts. The following is the result of this parent’s research.

NOTE:  The statistics  on this page have been updated as more responses have come in from school districts.

********************************************************************

Independent Survey of School Districts Claimed as Evidence of Investigations Success in 2007

The 2007 list of Investigations “Success Stories”  provided 70 school districts which, according to the publisher, had “experienced great success with Math Investigations”. Contacts with each school district resulted in the following:

• 62 of 70 districts responded
• 36 of those 62 have discontinued use or are in the process of discontinuing the use of Investigations (58% of districts responding)

The most common reasons cited for dropping Investigations were

• inadequate alignment with state standards
• large size of district made fidelity of implementation and ongoing professional development difficult
• flat lined or declining math and reading scores
• budgetary concerns with the need to hire math coaches / specialists at each school, extensive professional development requirements, and high materials costs

Twenty-Six districts report continued use of Investigations. Of those 26:

• 17 are Title I districts and receive NSF funding or other grants for continued implementation of the curricula (65% of responding districts still using Investigations)
• 8 use Investigations as their primary text with supplemental materials from other sources to fill gaps in content
• 2 use Investigations without supplementation
• 7 use Investigations as a supplement to other materials

The following trends were noted among responding districts still using Investigations either as a primary or supplemental text:

• many of these districts were small with fewer than 10 elementary schools making fidelity of implementation and support easier
• the teacher / student ratio in these district was quite low with average class sizes of 15 – 20 students
• many of the districts believe they needed to increase instructional time by 10 – 15 minutes per days for math because of Investigations
• grant monies were used by an increasing percentage of school districts to fund Investigations – especially in areas with a high percentage of title 1 schools

The full report can be found here

What Investigations teachers really think…..

about our children.

The following is an exert of a dissertation which appears on the TERC web site, entitled “Tidy Math Fan”. It was written in 2001 by Susan James, Grade 5 teacher, Winston-Salem, NC. I think the piece speaks for itself.

What is tidy math? Worksheets containing orderly rows of computation problems, all essentially the same problem, but with different numbers. Textbooks or teachers that cleanly demonstrate a method step by step and then ask students to do thirty problems using that same method. These are examples of tidy math.

Who are tidy math fans? Students who are neat and well-organized. Students who may not be too creative, but who pay attention and follow directions well. Students who are satisfied with knowing how and who are not bothered by not knowing why. Students who grow up, meet math teachers like myself at parties, and say “Oh, I’ve always liked math. I love how there’s always one right answer to a problem.” These are tidy math fans.

Tidy math fans do well in what we now call “traditional” math programs. But as some schools adopt new programs like Investigations, some of these students face a sudden drop in status, from one of the best math students in the class to an average, sometimes struggling student. Their self-esteem about their math ability plummets. It’s no wonder that some of their parents (who themselves grew up with tidy math) put up a fuss about the new program and teaching style that is causing their children’s loss of confidence.

Certainly not all students who enjoy tidy math are less successful with Investigations or similar programs. Some of them rise to the challenge and find that they are able to generate their own strategies instead of just following the teacher’s strategy, and that they actually feel better about what they are doing now that they understand why it works. But there are still some tidy math fans who do not adapt well. The rules for success and the very definition of what it means to do math have changed on them. Math is much harder now.

Can Investigations be blended?

A more important question, considering the discussion about blending Investigations which is scheduled for February 10th, is whether it is possible or even advisable to blend Investigations with other materials.    To figure that out you have to figure out what the differences between the approaches are and then examine those differences to see if they can be blended.

If you ignore all the rhetoric and debate about traditional and reform math and look at the details, you realize that the major differences between the two approaches fall into two broad categories – computational fluency and the introduction of standard processes and formulas.

The Investigations program follows the belief that learning the standard algorithms and math facts too soon inhibits the development of number sense and reasoning. Students in Investigations use what the authors call “transparent” algorithms to solve problems. Formal exposure to the standard algorithms is deferred until later grades and limited to comparing and contrasting the standard algorithms to the “transparent” algorithms taught in Investigations. The standard algorithms for addition and multiplication are studied in Investigations in Grade 4; the standard algorithms for subtraction is studied in grade 5. The standard algorithm for long division is not studied. PWCS has moved the lesson studying the standard algorithm for addition to Grade 3 and subtraction to Grade 4, but the nature and extent of the lessons are still limited to comparing and contrasting the standard algorithms to the “transparent” algorithms taught in Investigations.

Traditional math programs follow the belief that the standard algorithms are a primary computational tool, that learning them to the point of mastery allows students to explore more complex and abstract concepts. As such, traditional math programs teach the standard algorithms when students begin multi-digit addition and subtraction, generally in Grade 2. The standard algorithms are then practiced and reinforced to the point of mastery. Alternate computational strategies are taught, but only after the standard algorithms have been mastered.

How do you blend these two approaches when the philosophies which underlie them are so divergent? How do you adapt Investigations to provide direct instruction on the standard algorithms and ensure that it provides sufficient support and practice that the processes are mastered when the program is designed around the belief that learning those processes too early or to the point of mastery is dangerous?

You can’t.

The primary difference between the two philosophies is whether the standard algorithms are taught, the extent to which they are taught, and when they are taught.   When it comes to mathematics, programs are either traditional in that they teach the standard algorithms to the point of master to students beginning in Grade 2, or they are reform in that they teach alternate strategies and defer study of the standard algorithms to later grades.

Changing Investigations so that it teaches the standard algorithms to the point of mastery would require rejecting the “transparent” algorithms Investigations teaches and replacing them with direct instruction on the standard algorithms with materials obtained from other texts.  That would undermine the philosophy which underlies Investigations and, in the words of our staff, “When the sessions in Investigations are treated as separate activities to be selected or rejected, this careful continuity is lost, and student learning is jeopardized.”

That sentiment has been echoed multiple times by PWCS staff and TERC, the authors of Investigations.  In a February 2006  memo to Dr Walts, Pam Gauch, then Superintendent of Student Learning and Accountability, stated ” Research shows that student achievement will be better with the sole use of a traditional program or the sole use of a reform program than if both are used together.”

Our staff, in the document “Why are teachers asked to teach the Investigations program as it is written, rather than letting them choose from it?” , stated, “Research on program implementation cites inadequate fidelity of implementation as a major reason for program failure”.

Those comments seem to effectively close that debate – adapting Investigations by removing lessons and replacing them with lessons and materials obtaining from other texts will jeopardize student learning and increase the probability of program failure.

You may wonder about the commitments we’ve been hearing for the past several months about a blended approach to mathematics. What we’ve been calling a blended approach is nothing more than unadapted Investigations with a few additional lessons thrown in where necessary to meet SOL standards.

In lieu of the evidence of the inadvisability of changing the nature and structure of Investigations lessons, is creating a blended program with Investigations as the primary text something we really want to consider, or, is there another option to create a truly blended instructional program in PWC?

The opt in for traditional math seems to be that other option.  The textbook we used previously in PWC is much more flexible and amenable to adapting.  We could use that textbook as our primary textbook and supplement it with Investigations.  We could keep the Investigations program intact and the traditional program, which would be available to students at their parents request, would be developed to provide that blend of instructional materials we keep hearing about.  Yes, the opt in  program would be a traditional program because it would teach the standard algorithms and formulas to the point of mastery, but that doesn’t mean it would disregard conceptual understanding.

Where did I put that blend?

On February 10th the school board will be holding a math work session to discuss the opt in for traditional math and a blended instructional program. Several board members have expressed their support for a blended approach to instruction over an opt in.

That’s odd.   I thought we already had a blended approach to instruction, like these comments clearly indicate:

On March 5, 2008 Dr. Walts made the following statements in setting forth his expectations for the mathematics program in PWC elementary schools. “I support a balanced mathematics program. I think we are in the right direction in terms of the fact that our established curriculum has not changed and continues to be aligned with the Virginia Standards of Learning.”

“The good news, I think, is that the most recent adoption and, in fact, the new materials that we acquired this year actually is a blend of what I consider a balanced approach to mathematics.“

The December 2008 episode of “Inside Education” Discussed how “Carol Knight, supervisor of mathematics for the School Division, and Christine Bohannon, a second-grade teacher from Ashland Elementary School, join Blackstone for a discussion about how “Investigations in Number, Data and Space” is creating a blended approach to math instruction in PWCS elementary classrooms.”

In the September 2008 Program Evaluation Of Investigations the following recommendation was made regarding Instruction, “The Mathematics Office should continue to assist teachers, administrators, and parents in understanding that “Investigations” includes a balanced approach to mathematics by emphasizing conceptual understanding as well as mastery of facts and use of multiple strategies including traditional ones.”

In comments reported in the Washington Post following the September 2008 presentation of the 2 Year Program Evaluation Results, Chairman Johns was quoted as stating “Certainly, School Board members will keep tabs on math scores and continue to listen to concerns from parents and get updates on teachers’ professional development. But for right now, there’s no more formal activity on the agenda. We are taking a balanced approach, and we are seeing improvement in all groups and narrowing those gaps.”

Can someone please remind me why we’re discussing a blended approach to math instruction if we already, supposedly, have a blended approach?  And, what, exactly is a blended approach?

To me a blended approach would be one where material from other sources is added into  the existing lesson framework. So how have the Investigations lessons,which form the foundation of our math program, been adapted to include material from other sources?

I asked that exact question and was given a link to the pacing guides available on the PWCS web site.  So I decided to look at those pacing guides in detail, compare them to the Investigations program, and then review the planning calendars to see how extensive and time consuming the supplemental or adapted lessons are.

Our program is approximately 89% unadapted and unchanged Investigations.  Only about 11% of the lessons from Grades 1 – 4 are adapted to include supplemental material from sources other than Investigations and those materials aren’t necessarily traditional – they’re just from other sources.  None of the lessons on computation are adapted or supplemented with material outside of Investigations.

It’s kind of hard to see how that could be called blended.

The details are below.

Grade 1

There are approximately 172 instructional days in the 1st grade math calendar (count excludes holidays, teacher work days, and testing days); approximately 25 of those days contain supplemental lessons on topics such as telling time to the hour and half hour, money, volume, weight,  probability, and part to whole fractions (1/2, 1/3 and 1/4).  All other lessons are unadapted or include additional material which comes from Investigations.

That means that 15% of our 1st grade curriculum is from sources other than Investigations and the remaining 85% is unadapted Investigations.  Every one of those supplemental lessons, by the way, is necessary to meet minimum SOL standards for Grade 1.

Grade 2

There are approximately 173 instructional days in the second grade calendar (count excludes holidays, teacher work days, half days, and testing days); approximately 18 of those days include supplemental lessons on topics such as  data collection and analysis, probability, ordinals, rounding, money notation, 1/8 and 1/10, perimeter, volume, temperature, liquid volume, weight and mass.  All other lessons are unadapted or include additional material which comes from Investigations.

That means that approximately 10%  of our 2nd grade curriculum is from sources other than Investigations and the remaining 90% is unadapted Investigations.  Every one of those supplemental lessons, by the way, is necessary to meet minimum SOL standards for Grade 2.  It is also worth noting that the core Investigations lessons on computation are neither supplemented nor extended to include traditional computational strategies.

Grade 3

There are approximately 164 instructional days in the 3rd grade calendar (count excludes holidays, teacher work days, half days, SOL prep days, and testing days); approximately 20 of those days include supplemental lessons on topics such as : probability, equivalent period of time, patterns, input / output machines, liquid volume and weight, comparing and ordering fractions, decimal computation, and making change. All other lessons are unadapted or include additional material which comes from Investigations.

That means that approximately 12%  of our 3rd grade curriculum is from sources other than Investigations and the remaining 88% is unadapted Investigations.  Every one of those supplemental lessons, by the way, is necessary to meet minimum SOL standards for Grade 3.

It is worth noting that the core Investigations lessons on computation are neither supplemented nor extended to include traditional computational strategies.   It is also worth noting that the single lesson on the standard algorithm for addition is moved from Grade 4 to Grade 3 but is unchanged from the content described in this article.

Grade 4

There are approximately 163 instructional days in the 4th grade calendar (count excludes holidays, teacher work days, half days, SOL prep days, and testing days); approximately 10 of those days include supplemental lessons on topics such as : geographic patterns and function tables, coordinating geometry, transformations using patty paper, area and perimeter, and subtracting decimals.  All other lessons are unadapted or include additional material which comes from Investigations.

That means that approximately 6%  of our 4th grade curriculum is from sources other than Investigations and the remaining 94% is unadapted Investigations.

It is worth noting that the core Investigations lessons on computation are neither supplemented nor extended to include traditional computational strategies.   It is also worth noting that the single lesson on the standard algorithm for subtraction is moved from Grade 5 to Grade 4 but is unchanged from the content described in the article linked above.